Efficient prediction for linear and nonlinear autoregressive models

Müller, Ursula U. ; Schick, Anton ; Wefelmeyer, Wolfgang

Ann. Statist., Tome 34 (2006) no. 1, p. 2496-2533 / Harvested from Project Euclid

Résumé

Conditional expectations given past observations in stationary time series are usually estimated directly by kernel estimators, or by plugging in kernel estimators for transition densities. We show that, for linear and nonlinear autoregressive models driven by independent innovations, appropriate smoothed and weighted von Mises statistics of residuals estimate conditional expectations at better parametric rates and are asymptotically efficient. The proof is based on a uniform stochastic expansion for smoothed and weighted von Mises processes of residuals. We consider, in particular, estimation of conditional distribution functions and of conditional quantile functions.

Détail

Publié le : 2006-10-14
Classification:  Empirical likelihood,  Owen estimator,  weighted density estimator,  kernel smoothed empirical process,  functional central limit theorem,  Donsker class,  uniformly integrable entropy,  uniformly integrable bracketing entropy,  pseudo-observation,  plug-in-estimator,  AR model,  EXPAR model,  SETAR model,  62M20,  62G05,  62G20,  62M05,  62M10